Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons



• Closed plane figure
• At least 3 sides that are segments
• Sides intersect only at endpoints
• Adjacent sides are NOT collinear
POLYGONS NOT POLYGONS

• Start at any vertex
• List vertices consecutively
Name the polygon. Name the sides and angles.
B
A C
E D

Common Polygons:
SIDES NAME
10
12 n
8
9
3
4
5
6
Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
Nonagon
Decagon
Dodecagon
n- gon

CONVEX POLYGON
• No diagonal with points outside polygon
CONCAVE POLYGON
• At least one diagonal outside polygon

The sum of the measures of angles in an n-gon :
(n-2)180
Example:
Find the sum of the measures of a 15-gon.

• Figure out what the sum of the interior angles should be
• Add up expressions and set them equal to the sum from part one.
EXAMPLE: Find y: y°
120°
85° 53°

Example:
1. The sum of the measures of a given polygon is 720. How many sides are in the polygon?
2.Pentagon ABCDE has 5 congruent angles. Find the measure of each angle.

Polygon-Exterior-Angle Sum Theorem
The sum of the measures of exterior angles of a polygon is ALWAYS 360⁰ .
Example:
What is the sum of exterior angles for a 500-gon?

EQUILATERAL POLYGON:

EQUIANGULAR POLYGON: All angles

REGULAR POLYGON: equilateral and equiangular
ONE

ONE

( n

2 ) 180
360 n n

Examples:
1. The sum of the measures of angles of a polygon with n sides is 1980. Find n, the number of sides.
2. Find the measures of one interior angle and one exterior angle of a REGULAR hexagon.
3. The measure of an exterior angle of a regular polygon is 30⁰. What is the measure of an interior angle? How many sides are there?

TYPE 2: Write and answer the following on a separate piece of paper. (2 points each question)
1. Find the sum of the interior and exterior angles of an octagon.
2. Find the measure of one interior angle and one exterior angle of a REGULAR 15-gon.
3. The sum of the interior angles of a polygon is 4680°.
Find the number of sides.